Imprecision in modern day data has become a common feature and in order to efficiently handle them many uncertainty based models have been put forth in the literature. Rough set model introduced by Pawlak has established itself to be an efficient model in many real life situations. But the basic rough set model of Pawlak has limited applications because of the constraint of it being dependent on equivalence relations. The equivalent mathematical concept to equivalence relation is that of a partition. A cover is a generalization of the notion of partition and this led to the development of covering based rough sets, which has better modeling power than basic rough sets. Following the concepts of granular computing rough set introduced by Pawlak is single granulation. So, in order to handle multi-granularity, two types of multi-granularities called optimistic multi-granulation and pessimistic multi-granulation were introduced in 2006 and 2010 respectively. Recently these two concepts of multi-granulation and covering based rough sets were combined to define covering based multi-granular rough sets. The equality of sets in mathematics is too redundant to have any fruitful real life application as it does not include user knowledge into it, which is normally done in practice. In order to handle this rough equalities were defined by Pawlak et al, which was extended by Tripathy in2008 to define rough equivalence. In this paper we introduce and study covering based optimistic multi-granular approximate equalities and study their properties. We study two types of properties called general properties and replacement properties. A real life example is used for illustration of the concepts and also to aid in the construction of counter examples in the proofs of the properties. © 2015, Institute of Integrative Omics and Applied Biotechnology. All rights reserved.